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      SUBROUTINE <a name="DLASQ5.1"></a><a href="dlasq5.f.html#DLASQ5.1">DLASQ5</a>( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN,
     $                   DNM1, DNM2, IEEE )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      LOGICAL            IEEE
      INTEGER            I0, N0, PP
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   Z( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DLASQ5.20"></a><a href="dlasq5.f.html#DLASQ5.1">DLASQ5</a> computes one dqds transform in ping-pong form, one
</span><span class="comment">*</span><span class="comment">  version for IEEE machines another for non IEEE machines.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  I0    (input) INTEGER
</span><span class="comment">*</span><span class="comment">        First index.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N0    (input) INTEGER
</span><span class="comment">*</span><span class="comment">        Last index.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Z     (input) DOUBLE PRECISION array, dimension ( 4*N )
</span><span class="comment">*</span><span class="comment">        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
</span><span class="comment">*</span><span class="comment">        an extra argument.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  PP    (input) INTEGER
</span><span class="comment">*</span><span class="comment">        PP=0 for ping, PP=1 for pong.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU   (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        This is the shift.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN  (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        Minimum value of d.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN1 (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        Minimum value of d, excluding D( N0 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DMIN2 (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DN    (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        d(N0), the last value of d.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DNM1  (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        d(N0-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DNM2  (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment">        d(N0-2).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IEEE  (input) LOGICAL
</span><span class="comment">*</span><span class="comment">        Flag for IEEE or non IEEE arithmetic.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameter ..
</span>      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            J4, J4P2
      DOUBLE PRECISION   D, EMIN, TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( ( N0-I0-1 ).LE.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      J4 = 4*I0 + PP - 3
      EMIN = Z( J4+4 )
      D = Z( J4 ) - TAU
      DMIN = D
      DMIN1 = -Z( J4 )
<span class="comment">*</span><span class="comment">
</span>      IF( IEEE ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Code for IEEE arithmetic.
</span><span class="comment">*</span><span class="comment">
</span>         IF( PP.EQ.0 ) THEN
            DO 10 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-2 ) = D + Z( J4-1 )
               TEMP = Z( J4+1 ) / Z( J4-2 )
               D = D*TEMP - TAU
               DMIN = MIN( DMIN, D )
               Z( J4 ) = Z( J4-1 )*TEMP
               EMIN = MIN( Z( J4 ), EMIN )
   10       CONTINUE
         ELSE
            DO 20 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-3 ) = D + Z( J4 )
               TEMP = Z( J4+2 ) / Z( J4-3 )
               D = D*TEMP - TAU
               DMIN = MIN( DMIN, D )
               Z( J4-1 ) = Z( J4 )*TEMP
               EMIN = MIN( Z( J4-1 ), EMIN )
   20       CONTINUE
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Unroll last two steps.
</span><span class="comment">*</span><span class="comment">
</span>         DNM2 = D
         DMIN2 = DMIN
         J4 = 4*( N0-2 ) - PP
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM2 + Z( J4P2 )
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
         DMIN = MIN( DMIN, DNM1 )
<span class="comment">*</span><span class="comment">
</span>         DMIN1 = DMIN
         J4 = J4 + 4
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM1 + Z( J4P2 )
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
         DMIN = MIN( DMIN, DN )
<span class="comment">*</span><span class="comment">
</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Code for non IEEE arithmetic.
</span><span class="comment">*</span><span class="comment">
</span>         IF( PP.EQ.0 ) THEN
            DO 30 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-2 ) = D + Z( J4-1 )
               IF( D.LT.ZERO ) THEN
                  RETURN
               ELSE
                  Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
                  D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
               END IF
               DMIN = MIN( DMIN, D )
               EMIN = MIN( EMIN, Z( J4 ) )
   30       CONTINUE
         ELSE
            DO 40 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-3 ) = D + Z( J4 )
               IF( D.LT.ZERO ) THEN
                  RETURN
               ELSE
                  Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
                  D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
               END IF
               DMIN = MIN( DMIN, D )
               EMIN = MIN( EMIN, Z( J4-1 ) )
   40       CONTINUE
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Unroll last two steps.
</span><span class="comment">*</span><span class="comment">
</span>         DNM2 = D
         DMIN2 = DMIN
         J4 = 4*( N0-2 ) - PP
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM2 + Z( J4P2 )
         IF( DNM2.LT.ZERO ) THEN
            RETURN
         ELSE
            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
            DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
         END IF
         DMIN = MIN( DMIN, DNM1 )
<span class="comment">*</span><span class="comment">
</span>         DMIN1 = DMIN
         J4 = J4 + 4
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM1 + Z( J4P2 )
         IF( DNM1.LT.ZERO ) THEN
            RETURN
         ELSE
            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
            DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
         END IF
         DMIN = MIN( DMIN, DN )
<span class="comment">*</span><span class="comment">
</span>      END IF
<span class="comment">*</span><span class="comment">
</span>      Z( J4+2 ) = DN
      Z( 4*N0-PP ) = EMIN
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DLASQ5.193"></a><a href="dlasq5.f.html#DLASQ5.1">DLASQ5</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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